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PSAT Math : Arithmetic

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Example Questions

Example Question #131 : Arithmetic

Alternating1

Possible Answers:

$\dpi{100} -\frac{47}{60}$

$\dpi{100} \frac{47}{60}$

$\dpi{100} \frac{17}{60}$

$\dpi{100} \frac{43}{60}$

$\dpi{100} -\frac{43}{60}$

Correct answer:

$\dpi{100} \frac{47}{60}$

Explanation:

Alternating2

Alternating3

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Example Question #1 : How To Add Fractions

Solve $\frac{3}{7}+\frac{5}{8}-\frac{1}{2}$ .

Possible Answers:

$\frac{33}{56}$

$\frac{31}{56}$

$\frac{7}{8}$

$\frac{5}{7}$

Correct answer:

$\frac{31}{56}$

Explanation:

Finding the common denominator yields $\frac{24}{56}+\frac{35}{56}-\frac{28}{56}$ . We can then evaluate leaving $\frac{31}{56}$ .

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Example Question #2 : How To Add Fractions

What is the solution, reduced to its simplest form, for $x = \frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}}$ ?

Possible Answers:

$x = \frac{7}{15}$

$x = \frac{5}{3}$

$x = \frac{75}{45}$

$x =2$

$x = \frac{115}{45}$

Correct answer:

$x = \frac{5}{3}$

Explanation:

$x=\frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}=\frac{35}{45}+\frac{27}{45}+\frac{6}{45}+\frac{7}{45}=\frac{75}{45}=\frac{5}{3}$

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Example Question #3 : How To Add Fractions

What is the sum of $\small \frac{4}{5}$ and $\small 2 \frac{5}{6}$ ?

Possible Answers:

$\small \frac{49}{12}$

$\small \frac{49}{109}$

$\small \frac{79}{30}$

$\small \frac{30}{109}$

$\small \frac{109}{30}$

Correct answer:

$\small \frac{109}{30}$

Explanation:

We can begin by eliminating the obviously wrong answers. We know that the sum of the two fractions will be more than 1, so the answer choices $\tiny \tiny \frac{49}{109}$ and $\small \frac{30}{109}$ are out. Now, let's add the two fractions:

Begin by converting $\small 2 \frac{5}{6}$ to $\tiny \frac{17}{6}$ .

Now find the common denominator of $\small \frac{4}{5}$ and $\tiny \frac{17}{6}$ . The least common multiple of 5 and 6 is 30, so 30 is the common denominator. Now alter both fractions so that they use the common denominator:

$\tiny \small \frac{4}{5}= \frac{4*6}{5*6}=\frac{24}{30}$

$\tiny \small \frac{17}{6}=\frac{17*5}{6*5}=\frac{85}{30}$

Now we can easily add the two fractions together:

$\small \frac{24}{30}+\frac{85}{30}=\frac{109}{30}$

The answer is $\small \frac{109}{30}$ .

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Example Question #1 : How To Find The Reciprocal Of A Fraction

What is the reciprocal of the following fraction: 18/27

Possible Answers:

27/18

9/27

-18/27

Correct answer:

27/18

Explanation:

A fraction multiplied by its reciprocal will equal 1. To find the reciprocal of a fraction, switch the denominator and numerator. The reciprocal of 18/27 is 27/18.

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Example Question #1 : How To Find The Lowest / Least Common Denominator

3/5 + 4/7 – 1/3 =

Possible Answers:

3/37

7/9

88/105

4/3

72/89

Correct answer:

88/105

Explanation:

We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35.

Now to the subtraction. The lowest common denominator of 35 and 3 is 35 * 3 = 105, so altogether, 3/5 + 4/7 – 1/3 = 41/35 – 1/3 = 123/105 – 35/105 = 88/105. This does not simplify and is therefore the correct answer.

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Example Question #131 : Fractions

3/5 + 4/7 – 1/3 =

Possible Answers:

88/105

3/37

72/89

7/9

4/3

Correct answer:

88/105

Explanation:

We need to find a common denominator to add and subtract these fractions. Let's do the addition first. The lowest common denominator of 5 and 7 is 5 * 7 = 35, so 3/5 + 4/7 = 21/35 + 20/35 = 41/35.

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Example Question #1 : How To Find The Lowest / Least Common Denominator

$\textup{During a hike, Alexis completed }\frac{2}{5}\textup{ of a trail, took a short break, then }$

$\textup{walked another }\frac{3}{7}\textup{ of the trail. At this point, what fraction of the trail}$

$\textup{did Alexis stll have left to walk?}$

Possible Answers:

$\frac{8}{35}$

$\frac{1}{7}$

$\frac{1}{5}$

$\frac{6}{35}$

$\frac{2}{7}$

Correct answer:

$\frac{6}{35}$

Explanation:

$\textup{Find LCD: }5\times7=35\: \: \: \: \: \: \frac{2(7)}{5(7)}+\frac{3(5)}{7(5)}=\frac{14}{35}+\frac{15}{35}=\frac{29}{35}$

$\frac{35}{35}-\frac{29}{35}=\frac{6}{35}$

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Example Question #1 : How To Find The Lowest / Least Common Denominator

Simplify:

$\frac{7}{15}+\frac{2}{3}+\frac{13}{20}$

Possible Answers:

$\frac{57}{30}$

$\frac{22}{38}$

$\frac{107}{60}$

Correct answer:

$\frac{107}{60}$

Explanation:

First, find the common denominator of the fractions in order to add them together. Looking at the first two fractions, we can see that the common denominator is 15 because 3 times five is 15. We can now change both fractions to have a denominator of 15 so that we can add them together:

$\frac{7}{15}+\frac{2\cdot 5}{3\cdot 5}+\frac{13}{20}$

$\frac{7}{15}+\frac{10}{15}+\frac{13}{20}$

$\frac{17}{15}+\frac{13}{20}$

Now, find a common denominator for the remaining fractions. This can be done by listing multiples of 15 and 20 and finding the lowest common multiple:

15: 15, 30, 45, 60, 75

20: 20, 40, 60, 80

60 is the lowest common multiple, so it is our least common denominator.

$\frac{17\cdot 4}{15\cdot 4}+\frac{13\cdot 3}{20\cdot 3}$

$\frac{68}{60}+\frac{39}{60}$

$\frac{107}{60}$

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Example Question #1 : How To Find A Solution To A Compound Fraction

Simplify:

$\frac{56}{1-\frac{1}{49}}$

Possible Answers:

$54\frac{48}{49}$

$57 \frac{1}{6}$

$54\frac{6}{7}$

$55\frac{1}{49}$

$55\frac{1}{7}$

Correct answer:

$57 \frac{1}{6}$

Explanation:

$\frac{56}{1-\frac{1}{49}}$

$= 56 \div \left ( 1-\frac{1}{49} \right )$

$= 56 \div \left (\frac{49}{49} -\frac{1}{49} \right )$

$= \frac{56 }{1}\div \frac{48}{49}$

$= \frac{56 }{1}\cdot \frac{49}{48}$

$= \frac{7}{1}\cdot \frac{49}{6}$

$= \frac{343}{6}$

$= 57 \frac{1}{6}$

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PSAT Math : Arithmetic

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #131 : Arithmetic

Example Question #1 : How To Add Fractions

Example Question #2 : How To Add Fractions

Example Question #3 : How To Add Fractions

Example Question #1 : How To Find The Reciprocal Of A Fraction

Example Question #1 : How To Find The Lowest / Least Common Denominator

Example Question #131 : Fractions

Example Question #1 : How To Find The Lowest / Least Common Denominator

Example Question #1 : How To Find The Lowest / Least Common Denominator

Example Question #1 : How To Find A Solution To A Compound Fraction

All PSAT Math Resources

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